Type: Seminar

Distribution: World

Expiry: 7 Feb 2023

CalTitle1: On constrained Willmore surfaces in R^4

Auth: carberry@p723.pc (assumed)

Using quaternionic function theory, we present the Kodaira representation of conformal maps of compact Riemann surfaces to R^4. We reproduce the classical result, that the subspace of conformal maps inside the space of immersions has a singularity at the isothermic surfaces. Our approach allows us to prove the existence of minimizers of the Willmore functional without the assumption that the infimum of the Willmore functional is less than 8 pi. We present some generalisation of constrained Willmore tori, which allows to deform their spectral curves to the unique vacuum with zero Willmore energy. We want to use this to determine for any elliptic curve the minimum of the Willmore energy on the space of conformal maps to R^4.

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